调和方程边值问题的高效配置算法

An efficient collocation method for solving boundary value problems of harmonic equations

首先给出了用Poisson积分公式表示的调和方程边值问题的解.然后利用延拓思想将一般区域上的问题转化为圆域上的问题,进而获得了所需的Poisson积分方程.最后,介绍了求解调和方程边值问题的线性配置算法,并证明了这种算法具有至少O(h4)精度的逐点强超收敛性.表1,参9.

This paper first gives the solutions represented by Poisson integral formulas to the boundary value problems of harmonic equations.Then using extension idea,we transforms the problem on the common domain to that on the circular domain,and further obtains the Poisson integral equation needed.Finally,we introduces a linear collocation method for solving boundary value problems of harmonic equations,and proves that this method possesses ultraconvergence with at least O(h^4) accuracy in the pointwise sense.1tab.9refs.